Modelica extensions for Multi-Mode DAE Systems

Hilding Elmqvist
Dassault Systèmes AB, Ideon Science Park, Lund, Sweden

Sven Erik Matsson
Dassault Systèmes AB, Ideon Science Park, Lund, Sweden

Martin Otter
German Aerospace Center (DLR), Institute of System Dynamics and Control, Wessling, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp14096183

Ingår i: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Linköping Electronic Conference Proceedings 96:19, s. 183-193

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


This paper describes a proposal for modeling systems with multiple operating modes; such as changing a controller from nominal operation to startup or shutdown or describing failure situations where the model structure is changing (e.g. an electrical line or a mechanical shaft breaks). This is achieved by extending the Modelica 3.3 synchronous state machines to continuous-time state machines having continuous-time models as “states”. Every model can be a “state” of a state machine; and in particular certain acausal models. Currently; no new language element is needed for Modelica; but a generalized semantics for State Machines has to be introduced; such as “merge semantics for differential equations“. Symbolic transformations are still handled during translation; so the generated code is efficient and there is no run-time interpreter. On the other; this feature restricts the class of multi-mode systems that can be handled.


Multi-mode; failure simulation; dynamically changing states; continuous-time state machine; hybrid state machine.


Bastian J., Clauß C., Enge-Rosenblatt O., and Schneider P. (2010): MOSILAB – a Modelica solver for multi-physics problems with structural variability. 1st Conference on Multiphysics Simulation - Advanced Methods for Industrial Engineering 2010. Download: http://publica.fraunhofer.de/starweb/servlet.starweb?path=urn.web&search=urn:nbn:de:0011-n-1355711

Dassault Systèmes (2014): Dymola 2015 Alpha. http://www.Dymola.com

Elmqvist H., Gaucher F., Mattsson S.E., Dupont F. (2012): State Machines in Modelica. Modelica’2012 Conference, Munich, Germany, Sept. 3-5, 2012. Download: http://www.ep.liu.se/ecp/076/003/ecp12076003.pdf

Bouissou M., Elmqvist H., Otter M., and Benveniste A. (2014): Efficient Monte Carlo simulation of stochastic hybrid systems. Modelica’2014 Conference, Lund, Sweden, March 10-12.

Henzinger T.A. (1996): The Theory of Hybrid Automata. Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (LICS 96), pp. 278-292. DOI: 10.1109/LICS.1996.561342

Mattsson, S.E. and G. Söderlind (1993): Index reduction in differential-algebraic equations using dummy derivatives. SIAM Journal of Scientific and Statistical Computing, Vol. 14 pp. 677-692. DOI: 10.1137/0914043

Modelica Association (2012): The Modelica Language Specification, Version 3.3. Download: https://www.modelica.org/documents/ModelicaSpec33.pdf.

Pantelides C. (1988): The consistent initialization of differential-algebraic systems. SIAM Journal of Scientific and Statistical Computing, 9(2), pp. 213–231. DOI: 10.1137/0909014

Zimmer D. (2010): Equation-Based Modeling of Variable-Structure Systems. Dissertation, ETH Zürich, No. 18924. Download: http://www.inf.ethz.ch/personal/fcellier/PhD/zimmer_phd.pdf

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